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the awnser is 1

Amount of salt in 8ml                  =  (x%)(8ml)    Where 'x' is the % solution of the 8cc

amount of salt in 50% solution   =  .50 (9ml)

Amount of salt when finished in 42% solution  =   .42  (8+9ml)

Total salt to strat = total salt at end

8x + .5(9)  =  .42 (8+9)      Solve for 'x'

8x + 4.5   = 7.14

8x= 2.64

x = 2.64/8 = 33%  salt solution

No help needed anymore, I got the answer. Thanks!

0.0060466176 = 6.0466176e-3      approx

done on the web2.0 calc.

Help for domain please

\(log_2(x^2-5x)\le log_2(6x+12)\\ 2^{log_2(x^2-5x)}\le 2^{log_2(6x+12)}\\ x^2-5x\le 6x+12\\ x^2-5x-6x-12\le 0\\ x^2-11x-12\le 0\\ (x-12)(x+1)\le0\\ \text{Now graph or think about the graph of } y=(x-12)(x+1)\\ \text{The equality is true where } y \le 0\\ \text{This means the equality will be true for all x where the y value is under the x axis.}\)

Now

 y=(x-12)(x+1)

This is a concave up parabola which has x intercepts at  x=12 and x=-1

so it will be under the x axis between these values 

so

\(-1\le x\le12\)

If you need further explanation then ask for it :)

what is 8,569 rounded to 100

8,569 rounded to 100 is 8,570

  !

A gardener measures the height of a plant after 4 weeks to be 9.0 inches. After 6 weeks the height of the plant is 13.5 inches. In this situation, what UNITS would you use to describe the rate of change of the height of the plant?

The appropriate units are millimeters mm and hours h.

\(v=s/t\)

\(v=\frac{(13.5-9)inches}{(6-4)weeks}\)

\(v= \frac{4.5\ inches}{2\ weeks}\times\frac{25.4 \ mm}{inch}\times\frac{week}{7\times 24\ h}\)

\(\large v=0.34\frac{mm}{h}\)

   !

Part 1:

x(x + 5) = 24

Part 2:

x(x + 5) = 24

1st way: By trial and error(not recommended because in exam you will only get the marks for the answer but not the steps)

x = 3, (x+5) = 8

Therefore width = 3 inches and length = 8 inches.

x(x + 5) = 24

2nd way: By factorization(highly recommended if you are really good at factorization)

x^2 + 5x = 24

x^2 + 5x - 24 = 0

(x - 3)(x + 8) = 0

x = 3 or x = -8(rejected)

Therefore x = 3 and x + 5 = 8

Therefore width = 3 inches and length = 8 inches.

3rd way: By quadratic equation

x(x + 5) = 24

x^2 + 5x - 24 = 0

x = (- 5 +- sqrt(5^2 - 4*1*(-24)))/(2*1)

x = (-5 +- 8)/(2*1)

x = 3 or -8(rejected)

Therefore width = 3 inches and length = 8 inches

 ♪ ♪ Make the equation into slope-intercept form  ♪ ♪

0x + 6y = 35

6y = 35

y = 35/6

(You can say that the graph is a horizontal line at the height y = 35/6 already, but I will change it into y = mx + b)

y = 0x + 35/6

 ♪ ♪ Therefore the y-intercept = 35/6  ♪ ♪

Easy question. Good question though

We would use inches.

-4.5 x 10^7

= -45000000

All examples of composite numbers ending in 3 (1 - 500):

133 = 7 x 19

143 = 11 x 13 

203 = 7 x 29

253 = 11 x 23

323 = 17 x 19

343 = 7 x 7 x 7

403 = 13 x 31

413 = 7 x 59

473 = 11 x 43

493 = 17 x 29

This should be changed:

All numbers under 100 and ending in 3 except multiples of 3 are prime numbers.

Nth term =F + (N -1) x D, F=first term, N=number of terms, D=common difference.

50th term=-1 + (50 -1) x 0.5

                =-1 + (49 x0.5)

                =-1 + 24.50

                =23.50

Guest 1 shows the answer if you cannot use the numbers 1-20 more than once

If you CAN use the numbers more than once, it is MUCH larger

20 x 20 x 20 x 20 x 20 x 20 x 20 = 20^7 =20^7 = 1280000000      or     1: 1,280,000,000

Rearrange the equation in to   y = mx + b   form for a line and  'b' is the y-intercept

0x + 6y = 35

        6y = 0x +35

          y = 0x + 35/6            y intercept is  35 /6       this is just a straight horizontal line at y = 35/6 = 5 6/6

No.....it would be nice.   I use the Desmos online graphing calculator.

Slope =  (y2-y1)/(x2-x1)   =   (4-0)/(-9- -7)  =   -4/16

Part 1: Only these two: x(x + 5) = 24  and  (x + 5)(x) = 24

Part 2:

Area = Length x Width

Area =x(x + 5) =24

        =x^2 + 5x - 24 = 0, solve for x

Solve for x:
x^2 + 5 x - 24 = 0

The left hand side factors into a product with two terms:
(x - 3) (x + 8) = 0

Split into two equations:
x - 3 = 0 or x + 8 = 0

Add 3 to both sides:
x = 3 or x + 8 = 0

Subtract 8 from both sides:
Answer: |x = 3                  or                   x = -8

So the width =3 inches, and the length:

3 + 5 =8 inches.

Area = l x w     and area = 24 

Let length = x    then width = x+5

area = l * w     Substitue the values we have above

24 = x (x+5)       or   (x+5)x

Solve for x      24 = x(x+5)

24 = x^2 + 5x

0= x^2 + 5x -24

(x-3)(x+8) = 0         so x = 3  or -8 (throw this one out....you can't have length of -8)

                              so l= 3     w = l+5 = 8           8 x 3 = 24 in^2      CHECK!

The probabillity of guessing correctly should be:

1/20 x 1/19 x 1/18 x 1/17 x 1/16 x 1/15 x 1/14 =1: 390,700,800

23 is 92% of what number?

Let the number be N, then:

92% of N =23, 92% means=92/100, so we have:

0.92 x N = 23 divide both sides by 0.92

N =23 / 0.92

N = 25

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